Question: Solve for $x$ and $y$ using elimination. ${-3x+2y = 0}$ ${-5x-2y = -48}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-8x = -48$ $\dfrac{-8x}{{-8}} = \dfrac{-48}{{-8}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-3x+2y = 0}\thinspace$ to find $y$ ${-3}{(6)}{ + 2y = 0}$ $-18+2y = 0$ $-18{+18} + 2y = 0{+18}$ $2y = 18$ $\dfrac{2y}{{2}} = \dfrac{18}{{2}}$ ${y = 9}$ You can also plug ${x = 6}$ into $\thinspace {-5x-2y = -48}\thinspace$ and get the same answer for $y$ : ${-5}{(6)}{ - 2y = -48}$ ${y = 9}$